Data Flow

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Data Flow
04000-n.xxx 04000-1.p4p
sad.hkl sad.abs
04000-n.raw 04000-n._ls 04000-m.p4p
sad.prp name.ins name.hkl
name.ins
name.res name.lst
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Data Flow
SMART
04000-n.xxx 04000-1.p4p
sad.hkl sad.abs
XPREP
04000-n.raw 04000-n._ls 04000-m.p4p
sad.prp name.ins name.hkl
name.ins
name.res name.lst
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Data Flow
SMART
Information about Laue symmetry or
lattice centering
04000-n.xxx 04000-1.p4p
SADABS
sad.hkl sad.abs
SAINT
XPREP
04000-n.raw 04000-n._ls 04000-m.p4p
sad.prp name.ins name.hkl
name.ins
name.res name.lst
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Data Flow
Information about Laue symmetry or
lattice centering
04000-n.xxx 04000-1.p4p
sad.hkl sad.abs
04000-n.raw 04000-n._ls 04000-m.p4p
sad.prp name.ins name.hkl
name.ins
name.res name.lst
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Data Flow
Information about Laue symmetry or
lattice centering
04000-n.xxx 04000-1.p4p
sad.hkl sad.abs
04000-n.raw 04000-n._ls 04000-m.p4p
sad.prp name.ins name.hkl
name.ins
name.res name.lst
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Data Flow
name.hkl
name.ins
name.lst name.fcf name.cif name.pdb etc.
name.res
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Data Flow
name.hkl
name.ins
name.lst name.fcf name.cif name.pdb etc.
name.res
name.rtf
name.bmp
Paper / Grant proposal
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Structure Solution with SHELXS
SHELXS is a very automatic Black Box.
PATT solves a Patterson and is best for
structures with a few heavy atoms in combination
with many light atoms. Works very good in
centrosymmetric space groups. TREF uses direct
methods. You need atomic resolution (say 1.2 Å or
better). Read Sheldrick, G. M. Acta Cryst. Sect.
A (1990), 46, 467. Direct methods have problems
in the presence of inversion centers (use PATT or
solve in non-centrosymmetric space group and
transform by hand). Sometimes TREF 1000 (or 5000)
helps.
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Structure Refinement
The solution from SHELXS is frequently already
very good. However, the coordinates are not quite
accurate, the atom types of some or all atoms
have been assigned incorrectly (if at all), and
details of the structure are missing (H-atoms,
disorders, solvent molecules, etc.).
The atomic positions in the first . res file are
not the direct result of the diffraction
experiment, but an interpretation of the electron
density function calculated from the measured
intensities and the somehow determined phase
angles. Better phases can be calculated from the
atomic positions, which allow re-determining of
the electron density function with a higher
precision. From the new electron density map,
more accurate atomic positions can be derived,
which lead to even better phase angles, and so
forth.
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Structure Refinement
Close examination of the Fo-Fc map helps to
introduce new atoms and remove bad old ones.
Once all non-hydrogen atoms are found, the atoms
can be refined anisotropically. Once the model
is anisotropic, the hydrogen atom positions can
be determined or calculated.
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Evalution of the Model
The model should only be altered if a change
improves its quality. How to judge quality of
the model?
Least-squares approach By means of Fourier
transformation, a complete set of structure
factors is calculated from the atomic model. The
calculated intensities are then compared with the
measured intensities, and the best model is that,
which gives the smallest value for the
minimization function M.
or
F structure factor o observed c calculated
w weighting factor (derived from s).
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Refinement against F2 or F?
Past F Advantage Faster computing. Problems I
F2. That means extraction of a root! Difficult
for very weak reflections. Negative reflections
need to be ignored or arbitrarily set to a small
positive number. Estimation of s(F) from s(F2) is
very difficult. The least squares method is very
sensitive to the weights, which are calculated
from the standard uncertainties. Refinement
against F results in inaccuracies in the
refinement.
Now F2 Advantages none of the problems
mentioned arise. Disadvantage A little slower.
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Residual Values the R factors
wR2 Most closely related to refinement against
F2.
R1 Most popular one, based on F.
GooF S is supposed to be gt 1.0
F structure factor o observed c calculated
w weighting factor (derived from s). NR number
of independent reflections NP number of refined
parameters.
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Parameters
For every atom x, y, z coordinates and one
(isotropic) or six (anisotropic) displacement
parameters.
For every structure overall scale factor osf
(first FVAR). Possibly additional scale factors
(BASF, EXTI, SWAT, etc.). Possibly a
Flack-x-parameter.
Atom types are also parameters, even thought they
are not refined. Incorrectly assigned atom types
can cause quite some trouble.
Altogether The number of parameters is roughly
ten times the number of independent atoms in a
structure.
For a stable refinement data-to-parameter-ratio
should be gt 8 for non-centrosymmetric structures
and gt 10 for centrosymmetric structures. ? ca.
0.84 Å or 2T 50 (Mo).
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Constraints and Restraints
Both improve the data-to-parameter-ratio
Constraints remove parameters, restraints add
data.
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Constraints
Constraints are mathematical equations, relating
two or more parameters or assigning fixed
numerical values to certain parameters, hence
reducing the number of independent parameters to
be refined.
Site occupation factors are constraints present
in every structure. Even for disordered atoms the
sum of the occupancies is constrained to add up
to 1.0.
Atoms on special position require constraints for
their coordinates, occupancies and sometimes also
their ADPs
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Special Position Constraints
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Special Position Constraints
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Special Position Constraints
An atom on a twofold axis along b. A 180
rotation must not change the position of the atom
or the shape of the thermal ellipsoid. From the
first condition follows (x, y, z) (-x, y,
-z), which is only true for x z 0. The
second condition dictates (U11, U22, U33, U23,
U13, U12) (U11, U22, U33, -U23, U13, -U12),
which is only true for U23 U12 0.
No good
Good
SHELXL generates special positions
automatically. Big relief.
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Rigid Group Constraints
A group of atoms with known (or assumed)
geometry Refine six parameters (translation and
rotation) rather than 3N parameters for the
individual atoms (9N for anisotropic). A seventh
parameter can be refined as scale factor.
Typical examples Cp or Cp ligands, phenyl
rings, SO4-, perchlorate ions, etc.
In SHELXL AFIX mn / AFIX 0 command m describes
the geometry of the group and n the mathematical
treatment.
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Hydrogen Atoms
Only 1 delocalized electron. Hydrogen atoms can
be placed on mathematically calculated positions
and refined using a riding model.
That means X-H distances and H-X-H or H-X-Y
angles are constraint to certain values. Not the
hydrogen positions!
In SHELXL HFIX mn generates the appropriate
AFIX commands Again m describes the geometry of
the group and n the mathematical treatment.
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Other Constraints
EADP atom1 atom2 Forces the two atoms to have
identical ADPs
EXYZ atom1 atom2 Force the two atoms to have
identical oordinates.
EADP and EXYZ can be useful for disorders or the
refinement of mixed crystals (e.g. zeolithes).
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Next Meeting
Tuesday January 10, 2005,1115 a.m. MOORE room
(here)
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